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arxiv: 2512.02066 · v2 · submitted 2025-11-29 · 🪐 quant-ph · cs.AI· cs.LG· eess.IV

Parallel Multi-Circuit Quantum Feature Fusion in Hybrid Quantum-Classical Convolutional Neural Networks for Breast Tumor Classification

Ece Yurtseven This is my paper

Pith reviewed 2026-05-17 02:59 UTC · model grok-4.3

classification 🪐 quant-ph cs.AIcs.LGeess.IV
keywords hybrid QCNNquantum feature fusionbreast tumor classificationvariational quantum circuitsBreastMNISTmedical image classificationentanglementquantum machine learning
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The pith

A hybrid quantum-classical CNN improves breast tumor classification accuracy over a parameter-matched classical model by fusing features from two variational quantum circuits.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a hybrid quantum-classical convolutional neural network for binary classification of benign versus malignant breast tumors on the BreastMNIST dataset. Classical convolutional layers extract initial features that are then combined with embeddings produced by two separate four-qubit variational quantum circuits, one using amplitude encoding and the other using angle encoding with circular entanglement. The fused representation feeds a classical fully connected classifier. The hybrid model is constructed with the same total parameter count as a baseline classical CNN and trained under identical conditions. Across five independent runs the hybrid version records higher accuracy, supported by a one-sided Wilcoxon signed-rank test yielding p = 0.03125 and a large Cohen’s d effect size of 2.14.

Core claim

The hybrid QCNN integrates classical convolutional feature extraction with two distinct quantum circuits—an amplitude-encoding variational quantum circuit and an angle-encoding VQC circuit with circular entanglement, both implemented on four qubits. These circuits generate quantum feature embeddings that are fused with classical features to form a joint feature space, which is subsequently processed by a fully connected classifier. When parameter-matched against a baseline classical CNN and trained under identical conditions using the Adam optimizer and binary cross-entropy loss, the hybrid QCNN achieves statistically significant improvements in classification accuracy on the BreastMNIST dat

What carries the argument

Parallel multi-circuit quantum feature fusion, in which outputs from an amplitude-encoding VQC and an angle-encoding VQC with circular entanglement on four qubits are combined with classical convolutional features before the final classifier.

If this is right

  • Hybrid QCNN architectures can leverage entanglement and quantum feature fusion to enhance medical image classification tasks.
  • This work establishes a statistical validation framework for assessing hybrid quantum models in biomedical applications.
  • Pathways for scaling to larger datasets and deployment on near-term quantum hardware are identified.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same parallel-fusion pattern of amplitude and angle encodings could be tested on other medical imaging tasks such as chest X-ray or MRI classification.
  • If the gain persists under stricter capacity controls, the result would support the idea that distinct quantum encodings supply complementary representations unavailable to classical layers of equal size.
  • Running the identical architecture on actual quantum hardware would reveal how device noise affects the reported accuracy difference.

Load-bearing premise

That the accuracy improvement is caused by the quantum feature fusion and entanglement rather than unaccounted differences in optimization landscape or effective capacity, even after parameter matching.

What would settle it

Replacing both quantum circuits with classical layers that preserve the exact parameter count and observing whether the accuracy advantage over the baseline CNN disappears.

Figures

Figures reproduced from arXiv: 2512.02066 by Ece Yurtseven.

Figure 1
Figure 1. Figure 1: Representative training samples from the BreastMNIST [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Amplitude embedding variational quantum circuit [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: Our proposed hybrid quantum-classical convolutional [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Angle encoding variational quantum circuit with cir [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: Training and validation loss curves for Hybrid Quantum [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 5
Figure 5. Figure 5: Testing accuracy graph including both models [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Training and validation loss curves for Classical Model [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
read the original abstract

Quantum machine learning has emerged as a promising approach to improve feature extraction and classification tasks in high-dimensional data domains such as medical imaging. In this work, we present a hybrid Quantum-Classical Convolutional Neural Network (QCNN) architecture designed for the binary classification of the BreastMNIST dataset, a standardized benchmark for distinguishing between benign and malignant breast tumors. Our architecture integrates classical convolutional feature extraction with two distinct quantum circuits: an amplitude-encoding variational quantum circuit (VQC) and an angle-encoding VQC circuit with circular entanglement, both implemented on four qubits. These circuits generate quantum feature embeddings that are fused with classical features to form a joint feature space, which is subsequently processed by a fully connected classifier. To ensure fairness, the hybrid QCNN is parameter-matched against a baseline classical CNN, allowing us to isolate the contribution of quantum layers. Both models are trained under identical conditions using the Adam optimizer and binary cross-entropy loss. Experimental evaluation in five independent runs demonstrates that the hybrid QCNN achieves statistically significant improvements in classification accuracy compared to the classical CNN, as validated by a one-sided Wilcoxon signed rank test (p = 0.03125) and supported by large effect size of Cohen's d = 2.14. Our results indicate that hybrid QCNN architectures can leverage entanglement and quantum feature fusion to enhance medical image classification tasks. This work establishes a statistical validation framework for assessing hybrid quantum models in biomedical applications and highlights pathways for scaling to larger datasets and deployment on near-term quantum hardware.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The paper presents a hybrid Quantum-Classical Convolutional Neural Network (QCNN) for binary classification of benign vs. malignant breast tumors on the BreastMNIST dataset. It integrates classical convolutional feature extraction with two 4-qubit variational quantum circuits—one using amplitude encoding and the other angle encoding with circular entanglement. The quantum embeddings are fused with classical features before a fully connected classifier. The hybrid QCNN is parameter-matched to a classical CNN baseline, and both are trained identically with Adam optimizer and binary cross-entropy loss. Over five independent runs, the hybrid model shows statistically significant accuracy improvements, confirmed by a one-sided Wilcoxon signed-rank test (p = 0.03125) and large Cohen's d = 2.14. The authors suggest this demonstrates the value of quantum entanglement and feature fusion in medical imaging tasks.

Significance. Should the performance advantage prove attributable to the quantum elements after rigorous controls, the work would offer valuable empirical support for hybrid QCNNs in biomedical applications. The inclusion of statistical testing across multiple runs and effect size reporting provides a solid empirical basis. This could help establish benchmarks for evaluating quantum advantages in practical classification problems and inform approaches for larger-scale implementations on NISQ devices.

major comments (1)
  1. [Experimental Evaluation and Discussion] The manuscript asserts that the accuracy lift arises from the quantum feature fusion and entanglement in the two VQCs (see abstract). While parameter matching is used to equalize total trainable weights, this does not ensure comparable expressivity, as the quantum circuits introduce entanglement-induced correlations and potentially distinct gradient flows. No ablation replacing the VQCs with classical modules of equivalent non-linear capacity is reported, nor are gradient statistics or loss landscape comparisons provided. Consequently, the observed statistical significance (p = 0.03125, d = 2.14 over 5 runs) cannot be unambiguously attributed to quantum mechanisms rather than optimization differences. This issue is central to the paper's interpretive claims.
minor comments (3)
  1. [Abstract] The abstract omits circuit diagrams, exact layer counts, data split details, and clarification on simulation versus hardware execution, which would aid quick assessment of the experimental rigor.
  2. [Methods] Provide more precise descriptions of how the classical CNN architecture was constructed to achieve parameter matching, including the number of parameters in each component.
  3. [Results] Specify the exact accuracy values or other metrics (e.g., precision, recall) for both models across the runs to allow readers to assess the practical magnitude of the improvement.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and for emphasizing the need to more rigorously attribute the observed accuracy improvements to the quantum components rather than to differences in optimization or expressivity. We address the major comment below and describe the revisions we will make.

read point-by-point responses

  1. Referee: [Experimental Evaluation and Discussion] The manuscript asserts that the accuracy lift arises from the quantum feature fusion and entanglement in the two VQCs (see abstract). While parameter matching is used to equalize total trainable weights, this does not ensure comparable expressivity, as the quantum circuits introduce entanglement-induced correlations and potentially distinct gradient flows. No ablation replacing the VQCs with classical modules of equivalent non-linear capacity is reported, nor are gradient statistics or loss landscape comparisons provided. Consequently, the observed statistical significance (p = 0.03125, d = 2.14 over 5 runs) cannot be unambiguously attributed to quantum mechanisms rather than optimization differences. This issue is central to the paper's interpretive claims.

    Authors: We agree that matching the total number of trainable parameters does not guarantee equivalent expressivity or identical optimization dynamics, given the presence of entanglement and the distinct structure of variational quantum circuits. Our design intentionally employs two complementary 4-qubit VQCs (amplitude encoding and angle encoding with circular entanglement) whose outputs are fused with classical features, and the statistical tests (Wilcoxon p=0.03125, Cohen's d=2.14) demonstrate a consistent advantage over the parameter-matched classical CNN under identical training conditions. However, we acknowledge that without explicit ablations that replace the VQCs by classical non-linear modules of comparable capacity, or without reporting gradient statistics and loss-landscape comparisons, alternative explanations cannot be excluded. In the revised manuscript we will add (i) an ablation study in which the two VQCs are replaced by classical dense layers with non-linear activations while preserving both parameter count and overall architecture depth, (ii) summary statistics of gradient norms across the five independent runs for both models, and (iii) a concise discussion of these controls together with their implications for interpreting the quantum contribution. These additions will directly address the central interpretive concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claim is direct experimental measurement

full rationale

The paper presents a hybrid QCNN architecture for BreastMNIST classification and reports empirical accuracy improvements over a parameter-matched classical CNN across five runs, supported by Wilcoxon signed-rank test (p=0.03125) and Cohen's d=2.14. No derivation chain, first-principles result, or predictive equation is claimed that reduces by construction to the paper's own inputs, fitted parameters, or self-citations. The architecture (amplitude and angle encoding VQCs with fusion) consists of design choices whose performance is measured directly rather than derived tautologically. This is self-contained empirical work; the statistical validation stands independent of any internal reduction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The paper relies on standard assumptions of variational quantum circuit simulation for small qubit counts and conventional neural network training; no new physical entities are introduced.

free parameters (2)
  • qubit count = 4
    Fixed at four qubits for both quantum circuits to enable classical simulation and near-term relevance.
  • number of independent runs = 5
    Set to five to support the Wilcoxon signed-rank test.
axioms (1)
  • domain assumption Quantum circuits with four qubits can be faithfully simulated on classical hardware without loss of the claimed advantage
    Implicit in the experimental setup; no actual quantum device execution is described.

pith-pipeline@v0.9.0 · 5576 in / 1403 out tokens · 56647 ms · 2026-05-17T02:59:58.188532+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On the Complementarity of Quantum and Classical Features: Adaptive Hybrid Quantum-Classical Feature Fusion for Breast Cancer Classification

    cs.CV 2026-04 unverdicted novelty 4.0

    A temperature-scaled hybrid fusion of ResNet and trainable quantum circuit features reaches 87.82% accuracy on BreastMNIST, outperforming classical baselines.

Reference graph

Works this paper leans on

26 extracted references · 26 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    Current and future burden of breast cancer: Global statistics for 2020 and 2040,

    M. Arnold, E. Morgan, H. Rumgay, A. Mafra, D. Singh, M. Laversanne, J. Vignat, J. R. Gralow, F. Cardoso, S. Sieslinget al., “Current and future burden of breast cancer: Global statistics for 2020 and 2040,”The Breast, vol. 66, pp. 15–23, 2022

    work page 2020

  2. [2]

    Global patterns and trends in breast cancer incidence and mortality across 185 countries,

    J. Kim, A. Harper, V . McCormack, H. Sung, N. Houssami, E. Morgan, M. Mutebi, G. Garvey, I. Soerjomataram, and M. M. Fidler-Benaoudia, “Global patterns and trends in breast cancer incidence and mortality across 185 countries,”Nature Medicine, pp. 1–9, 2025

    work page 2025

  3. [3]

    Mammography diagnosis of breast cancer screening through machine learning: a systematic review and meta-analysis,

    J. Liu, J. Lei, Y . Ou, Y . Zhao, X. Tuo, B. Zhang, and M. Shen, “Mammography diagnosis of breast cancer screening through machine learning: a systematic review and meta-analysis,”Clinical and Experi- mental Medicine, vol. 23, no. 6, pp. 2341–2356, 2023

    work page 2023

  4. [4]

    Deep convolutional neural networks in medical image analysis: A review,

    I. D. Mienye, T. G. Swart, G. Obaido, M. Jordan, and P. Ilono, “Deep convolutional neural networks in medical image analysis: A review,” Information, vol. 16, no. 3, p. 195, 2025

    work page 2025

  5. [5]

    Quantum machine learning,

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum machine learning,”Nature, vol. 549, no. 7671, pp. 195–202, 2017

    work page 2017

  6. [6]

    Quantum convo- lutional neural network based on variational quantum circuits,

    L.-H. Gong, J.-J. Pei, T.-F. Zhang, and N.-R. Zhou, “Quantum convo- lutional neural network based on variational quantum circuits,”Optics Communications, vol. 550, p. 129993, 2024

    work page 2024

  7. [7]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010

    work page 2010

  8. [8]

    Quantum algorithms for supervised and unsupervised machine learning

    S. Lloyd, M. Mohseni, and P. Rebentrost, “Quantum algorithms for supervised and unsupervised machine learning,”arXiv preprint arXiv:1307.0411, 2013

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  9. [9]

    Variational quantum algorithms,

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincioet al., “Variational quantum algorithms,”Nature Reviews Physics, vol. 3, no. 9, pp. 625– 644, 2021

    work page 2021

  10. [10]

    Supervised learning with quantum- enhanced feature spaces,

    V . Havl ´ıˇcek, A. D. C ´orcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, and J. M. Gambetta, “Supervised learning with quantum- enhanced feature spaces,”Nature, vol. 567, no. 7747, pp. 209–212, 2019

    work page 2019

  11. [11]

    Understanding the effects of data encoding on quantum- classical convolutional neural networks,

    M. Monnet, N. Chaabani, T.-A. Dr ˘agan, B. Schachtner, and J. M. Lorenz, “Understanding the effects of data encoding on quantum- classical convolutional neural networks,” in2024 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 1. IEEE, 2024, pp. 1436–1446

    work page 2024

  12. [12]

    Hybrid quantum-classical convolutional neural networks,

    J. Liu, K. H. Lim, K. L. Wood, W. Huang, C. Guo, and H.-L. Huang, “Hybrid quantum-classical convolutional neural networks,”Sci- ence China Physics, Mechanics & Astronomy, vol. 64, no. 9, p. 290311, 2021

    work page 2021

  13. [13]

    An image classification algorithm based on hybrid quantum classical convolutional neural network,

    W. Li, P.-C. Chu, G.-Z. Liu, Y .-B. Tian, T.-H. Qiu, and S.-M. Wang, “An image classification algorithm based on hybrid quantum classical convolutional neural network,”Quantum Engineering, vol. 2022, no. 1, p. 5701479, 2022

    work page 2022

  14. [14]

    Quantum machine learning for the future medical analysis: A comprehensive review and future prospects,

    B. L. R, J. R. J, S. S. C, and N. G, “Quantum machine learning for the future medical analysis: A comprehensive review and future prospects,” in2024 9th International Conference on Communication and Electronics Systems (ICCES), 2024, pp. 1256–1261

    work page 2024

  15. [15]

    Quantum data encoding: A comparative analysis of classical-to-quantum mapping techniques and their impact on machine learning accuracy,

    M. Rath and H. Date, “Quantum data encoding: A comparative analysis of classical-to-quantum mapping techniques and their impact on machine learning accuracy,”EPJ Quantum Technology, vol. 11, no. 1, p. 72, 2024

    work page 2024

  16. [16]

    Quantum classical hybrid convolutional neural networks for breast cancer diagnosis,

    Q. Xiang, D. Li, Z. Hu, Y . Yuan, Y . Sun, Y . Zhu, Y . Fu, Y . Jiang, and X. Hua, “Quantum classical hybrid convolutional neural networks for breast cancer diagnosis,”Scientific Reports, vol. 14, no. 1, p. 24699, 2024

    work page 2024

  17. [17]

    Breast cancer detection with quanvolutional neural networks,

    N. Matondo-Mvula and K. Elleithy, “Breast cancer detection with quanvolutional neural networks,”Entropy, vol. 26, no. 8, p. 630, 2024

    work page 2024

  18. [18]

    Quantum convolutional neural network: A hybrid quantum-classical approach for iris dataset classification,

    S. Tomal, A. A. Shafin, A. Afaf, and D. Bhattacharjee, “Quantum convolutional neural network: A hybrid quantum-classical approach for iris dataset classification,”arXiv preprint arXiv:2410.16344, 2024

    work page arXiv 2024

  19. [19]

    Hqcnn: A hybrid quantum-classical neural network for medical image classification,

    J. K. Fahim, P. C. Paul, M. R. Hossain, M. T. Ahmed, D. Chakraborty et al., “Hqcnn: A hybrid quantum-classical neural network for medical image classification,”arXiv preprint arXiv:2509.14277, 2025

    work page arXiv 2025

  20. [20]

    Enhanced hybrid quantum neural network for breast cancer detection,

    R. C. Rifat, M. T. U. I. Tonmoy, R. T. Aziz, and M. A. Qayum, “Enhanced hybrid quantum neural network for breast cancer detection,” in2024 27th International Conference on Computer and Information Technology (ICCIT). IEEE, 2024, pp. 1464–1469

    work page 2024

  21. [21]

    Parallel hybrid networks: an interplay between quantum and classical neural networks,

    M. Kordzanganeh, D. Kosichkina, and A. Melnikov, “Parallel hybrid networks: an interplay between quantum and classical neural networks,” Intelligent Computing, vol. 2, p. 0028, 2023

    work page 2023

  22. [22]

    Parallel proportional fusion of a spiking quantum neural network for optimizing image classification,

    Z. Xu, K. Shen, P. Cai, T. Yang, Y . Hu, S. Chen, Y . Zhu, Z. Wu, Y . Dai, J. Wanget al., “Parallel proportional fusion of a spiking quantum neural network for optimizing image classification,”Applied Intelligence, vol. 54, no. 22, pp. 11 876–11 891, 2024

    work page 2024

  23. [23]

    Hybrid quantum-classical convolutional neural network model for image classification,

    F. Fan, Y . Shi, T. Guggemos, and X. X. Zhu, “Hybrid quantum-classical convolutional neural network model for image classification,”IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 12, pp. 18 145–18 159, 2024

    work page 2024

  24. [24]

    Medmnist v2-a large-scale lightweight benchmark for 2d and 3d biomedical image classification,

    J. Yang, R. Shi, D. Wei, Z. Liu, L. Zhao, B. Ke, H. Pfister, and B. Ni, “Medmnist v2-a large-scale lightweight benchmark for 2d and 3d biomedical image classification,”Scientific Data, vol. 10, no. 1, p. 41, 2023

    work page 2023

  25. [25]

    Medical image diagnosis based on adaptive hybrid quantum cnn,

    N. Ajlouni, A. ¨Ozyavas ¸, M. Takao˘glu, F. Takao ˘glu, and F. Ajlouni, “Medical image diagnosis based on adaptive hybrid quantum cnn,”BMC Medical Imaging, vol. 23, no. 1, p. 126, 2023

    work page 2023

  26. [26]

    Quantum computing in the nisq era and beyond,

    J. Preskill, “Quantum computing in the nisq era and beyond,”Quantum, vol. 2, p. 79, 2018

    work page 2018